Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-12-01T07:38:50.423Z Has data issue: false hasContentIssue false
  • English
  • Français

Torque distribution optimization of redundantly actuated planar parallel mechanisms based on a null-space solution

Published online by Cambridge University Press:  15 January 2014

Jung Hyun Choi ,
TaeWon Seo  and
Jeh Won Lee
Jung Hyun Choi
Affiliation:
School of Mechanical Engineering, Yeungnam University, Gyeongsan 712-749, Republic of Korea
TaeWon Seo
Affiliation:
School of Mechanical Engineering, Yeungnam University, Gyeongsan 712-749, Republic of Korea
Jeh Won Lee*
Affiliation:
School of Mechanical Engineering, Yeungnam University, Gyeongsan 712-749, Republic of Korea
*
*Corresponding author. E-mail: jwlee@yu.ac.kr
Get access Rights & Permissions [Opens in a new window]

Summary

Redundant actuation for the parallel kinematic machine (PKM) is a well-known technique for overcoming general drawbacks of the PKM by helping it to avoid singularity and enhance stiffness characteristics, among others. Torque distribution plays a critical role in redundant actuation because this actuation causes the PKM to consume too much energy or put a substantial amount of stress on joints and links. This paper proposes a new torque distribution method for reducing the maximum torque of the actuator of a planar PKM. Here the main idea behind the proposed method is the use of superposition of a particular solution for a non-redundant case and an optimized null-space solution for a redundant case with a constant coefficient. The optimal value of a null-space solution can be easily determined by checking only the intersection points of the profile of the actuator's torque as the coefficient varies. We consider three cases of planar PKMs—2-, 3-, and 4-RRR PKMs—and present a detailed procedure for deriving a kinematic solution for the 2-RRR PKM based on Screw theory. We compare the proposed method with the minimum-norm pseudo-inverse method and assess a limitation of the proposed method. The torque distribution algorithm can be used to determine the number of actuators in an efficient manner and to reduce energy consumption.

Keywords

Torque distributionOptimizationRedundant actuationParallel mechanismParticular solutionNull-space solution
Type
Articles
Information
Robotica , Volume 32 , Issue 7 , October 2014 , pp. 1125 - 1134
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Seo, T., Kang, D. S., Kim, H. S. and Kim, J., “Dual servo control of a high-tilt 3-DOF micro parallel positioning platform,” IEEE-ASME Trans. Mechatronics 14 (5), 616–625 (2009).Google Scholar
2.Lee, D., Kim, J. and Seo, T., “Optimal design of 6-DOF eclipse mechanism based on task-oriented workspace,” Robotica 30 (7), 1041–1048 (2012).CrossRefGoogle Scholar
3.In, W., Lee, S., Jeong, J. I. and Kim, J., “Design of a planar-type high speed parallel mechanism positioning platform with the capability of 180 degrees orientation,” CIRP Ann. Manuf. Technol. 57 (1), 421–424 (2008).CrossRefGoogle Scholar
4.Shin, H., Lee, S., Jeong, J. I. and Kim, J., “Antagonistic stiffness optimization of redundantly actuated parallel manipulators in a pre-defined workspace,” IEEE/ASME Trans. Mechatronics 18 (3), 1161–1169 (2013).CrossRefGoogle Scholar
5.Jeong, J., Kang, D., Cho, Y. M. and Kim, J., “Kinematic calibration for redundantly actuated parallel mechanism,” J. Mech. Des. Trans. ASME 126 (2), 307–318 (2004).Google Scholar
6.Jeon, D., Kim, K., Jeong, J. I. and Kim, J., “A calibration method of redundantly actuated parallel mechanism machines based on projection technique,” CIRP Ann. Manuf. Technol. 59 (1), 413–416 (2010).Google Scholar
7.Kock, S. and Schumacher, W., “A Parallel X-Y Manipulator with Actuation Redundancy for High-Speed and Active-Stiffness Applications,” Proceedings of the IEEE International Conference on Robotics and Automation, Leuven, Belgium (1998) pp. 2295–2300.Google Scholar
8.Park, D. I., Lee, S. H., Kim, S. H. and Kwak, Y. K., “Torque distribution using a weighted pseudoinverse in a redundantly actuated mechanism,” Adv. Robot. 17, 807–820 (2003).CrossRefGoogle Scholar
9.Shim, H.-S., Seo, T. and Lee, J. W., “Optimal torque distribution method for a redundant 3-RRR parallel robot using a geometrical analysis,” Robotica 31 (4), 549–554 (2013).Google Scholar
10.Kim, S., Minimum Consumed Energy Optimized Trajectory Planning for Redundant Parallel Manipulator, Ph.D. Thesis (Seoul National University, 2010).Google Scholar
11.Ma, S., Hirose, S. and Nenchev, D. N., “Improving local torque optimization techniques for redundant robotic mechanisms,” J. Robot. Syst. 8 (1), 75–91 (1991).CrossRefGoogle Scholar
12.Suh, K. and Hollerbach, J., “Local Versus Global Torque Optimization of Redundant Manipulators,” Proceedings of the IEEE International Conference on Robotics and Automation, Raleigh, NC, USA (1987) pp. 619–624.Google Scholar
13.Maciejewski, A. A., “Real-Time SVD for the Control of Redundant Robotic Manipulators,” Proceedings of the IEEE International Conference on Systems Engineering, Dayton, OH, USA (1989) pp. 549–552.Google Scholar
14.Nokleby, S. B., Fisher, R., Podhorodeski, R. P. and Firmani, F., “Force capabilities of redundantly-actuated parallel manipulators,” Mech. Mach. Theory 40 (5), 578–599 (2005).CrossRefGoogle Scholar
15.Wu, J., Wang, J. and Wang, L., “A comparison of two planar 2-DOF parallel mechanisms: one with 2-RRR and the other with 3-RRR structures,” Robotica 28 (6), 937–942 (2010).CrossRefGoogle Scholar
16.Yong, Y. K. and Lu, T.-F., “Kinetostatic modeling of 3-RRR compliant micro-motion stages with flexure hinges,” Mech. Mach. Theory 44 (6), 1156–1175 (2009).CrossRefGoogle Scholar
17.Wu, J., Wang, J., Wang, L. and You, Z., “Performance comparison of three planar 3-DOF manipulator with 4-RRR, 3-RRR, and 2-RRR structure,” Mechatronics 20 (4), 510–517 (2010).Google Scholar
18.Duffy, J., Statics and Kinematics with Application to Robotics (Cambridge University Press, Cambridge, UK, 1996).Google Scholar
19.Strang, G., Introduction to Linear Algebra (Wellesley Cambridge Press, 2003).Google Scholar
20.Choi, J. H. and Lee, J. W., “Kinematic Analysis and Drive of 3DOF Parallel Manipulator,” Proceedings of the Joint Symposium of the Sister University of Mechanical University, Nagasaki, Japan (2012) pp. 73–76.Google Scholar
21.Spong, M. W., Hutchinson, S. and Vidyasagar, M., Robot Dynamics and Control (Wiley, 2005) pp. 73–117.Google Scholar
22.Park, F. C. and Kim, J. W., “Singularity analysis of closed kinematic chains,” ASME J. Mech. Des. 121 (1), 32–38 (1998).Google Scholar